We will investigate a class of singularities which occur in Einstein's general relativity and see if they can be resolved in quantum theory. We will consider several methods in differential geometry and, time-permitting, see some research by midshipmen in this area.

Bradley Efron characterized resampling methods as a way to “substitut[e] computational power for theoretical analysis” with the following payoff: “freedom from the constraints of traditional parametric theory, with its overreliance on a small set of standard models for which theoretical solutions are available.” In this talk I will introduce three resampling techniques commonly used today in statistical practice: bootstrapping, cross-validation, and permutation tests. After briefly presenting underlying theories, I’ll illustrate each technique by example. As time permits, I’ll introduce a new graph-theoretic approach to two-sample change detection problems as a current application of permutation testing.

This talk is a whirlwind tour of results from probability and statistics that I find interesting. Time permitting, we'll talk about the Central Limit Theorem and generalizations, the Berry-Esseen Theorem, the German Tank Problem, the Secretary Problem, how to win at H-O-R-S-E and/or darts, Polya's Recurrence Theorem, Bayes' Theorem for exponential families (conjugacy), etc.

This talk will introduce considerations for acoustic signal generation, propagation, and detection in the undersea environment. Topics will include the acoustic wave equation, the physical factors that affect sound speed in the ocean, measurement techniques, sonar equations, tactical implications, and a brief discussion of the contributions of array theory and nonlinear acoustics to the undersea environment.

In Isaac Asimov's "Foundation" novel, a scientist predicts the fall and rise of a galactic civilization using a branch of mathematics called physchohistory---a type of dynamical systems model to predict human nature. This got me thinking about what it would take to apply mathematical models to social science fields, which got me questioning what a mathematical model really is. In this talk, I will try to aggregate as much information and as many examples as possible to explore what a mathematical model is, what they are used for, and what makes a good model. In addition, I will also touch on what an OR and Statistical model is. Beware: this talk will be philosophical in nature.

curl(grad f) = 0 and div(curl F) = 0. Is there a vector field whose curl vanishes which is not the gradient of anything, or a vector field whose divergence vanishes which is not the curl of anything? The answer lies in topology.